Abstract

Measurements of scattering/extinction and asymmetry ratios at both polarization orientations, along with depolarization and reciprocity ratios, corresponding to nanosized Fe2O3 aggregates were carried out in an Fe(CO)5-seeded CO air-diffusion flame as a function of the position above the burner surface. The measurements were combined with an exact light-scattering theory to yield, for the first time, the complex refractive index, the primary particle-size parameter, the aspect ratio, and the number density and volume fractions of the Fe2O3 chainlike aggregates under flame conditions. An effective complex refractive index of 1.96 ± 6.9% to 0.20 ± 14.5% was inferred from the data analysis at a wavelength of 488 nm and in the temperature range of 894–924K. The corresponding primary particle size was found to be 48 nm ± 13%, and the aggregate aspect ratio was in the range of 6–7. Comparisons of the size parameters are made with transmission electron microscopy results, and the possible sources of uncertainties in the inferred results pertaining to temperature, polydispersity effects, and the departure from the straight configuration are discussed.

© 2003 Optical Society of America

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References

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  1. G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News 62(32), 22–29 (1984).
    [CrossRef]
  2. S. E. Pratsinis, S. V. R. Mastrangelo, “Material synthesis in aerosol reactors,” Chem. Eng. Prog. 85(5), 62–66 (1989).
  3. G. D. Ulrich, N. S. Subramanian, “Particle growth in flames III. Coalescence as a rate controlling process,” Combust. Sci. Technol. 17, 119–125 (1977).
    [CrossRef]
  4. D. W. Hahn, T. T. Charalampopoulos, “The role of iron additive in sooting premixed flames,” in Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Sydney, Sydney, Australia, 1992), pp. 1007–1014.
  5. T. T. Charalampopoulos, D. W. Hahn, H. Chang, “Role of metal additives in light scattering from flame particulates,” Appl. Opt. 31, 6519–6528 (1992).
    [CrossRef]
  6. I. A. Medalia, F. A. Heckman, “Morphology of aggregates II. Size and shape factors of carbon black aggregates from electron microscopy,” Carbon 7, 567–582 (1969).
    [CrossRef]
  7. G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
    [CrossRef] [PubMed]
  8. J. Allen, R. B. Husar, E. S. Macias, “Aerosol size and shape distribution using a laser scattering spectrometer,” in Aerosol Measurements, F. S. Harris, W. H. Harlow, M. Lippman, W. E. Clark, M. D. Durham, eds., pp. 312–330.
  9. O. Preining, “The Stokes diameter of ellipsoidal particles,” Atmos. Environ. 1, 271–285 (1967).
    [CrossRef]
  10. H. Rohatschek, “Direction, magnitude, and causes of photophoretic forces,” J. Aerosol Sci. 16, 29–42 (1985).
    [CrossRef]
  11. P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
    [CrossRef]
  12. T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Progress Energy Combust. Sci. 18, 13–45 (1992).
    [CrossRef]
  13. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983).
  14. H. C. van Hulst, Light Scattering by Small ParticlesDover, New York, 1981.
  15. C. F. Bohren, D. R. Hufman, Absorption and Scattering by Small Particles (Wiley, New York, 1983).
  16. R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
    [CrossRef] [PubMed]
  17. G. M. Faeth, Ü. Ö. Köylü, “Soot morphology and optical properties in nonpremixed turbulent flame environments,” Combust. Sci. Technol. 108, 207–229 (1995).
    [CrossRef]
  18. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  19. W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1995).
    [CrossRef]
  20. W. Lou, T. T. Charalampopoulos, “On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation,” J. Phys. D 28, 2585–2594 (1995).
    [CrossRef]
  21. G. Shu, T. T. Charalampopoulos, “Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols,” Appl. Opt. 39, 6713–6724 (2000).
    [CrossRef]
  22. G. Shu, T. T. Charalampopoulos, “Reciprocity theorem for the calculation of average properties of agglomerated particles,” Appl. Opt. 39, 5827–5833 (2000).
    [CrossRef]
  23. T. T. Charalampopoulos, G. Shu, “Effects of polydispersity of chainlike aggregates on light-scattering properties and data inversion,” Appl. Opt. 41, 723–733 (2002).
    [CrossRef] [PubMed]
  24. G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
    [CrossRef] [PubMed]
  25. Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty Sixth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Naples, Naples, Italy, 1996), pp. 1851–1858.
  26. T. T. Charalampopoulos, “An automated light scattering system and a method for the measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
    [CrossRef]
  27. http://www.lbl.gov/Publications/LDRD/1996/Charych.html
  28. R. R. Rudder, D. R. Bach, “Rayleigh scattering of ruby-laser light by neutral gases,” J. Opt. Soc. Am. 58, 1260 (1968).
    [CrossRef]
  29. H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
    [CrossRef]
  30. B. J. Stagg, “Development of a technique to determine the temperature dependence of the refractive index of carbonaceous particulates,” Ph.D. dissertation (Louisiana State University, Baton Rouge Campus, Baton Rouge, La., 1992).
  31. S. C. Lee, C. L. Tien, “Effects of soot shape on soot radiation,” J. Quant. Spectrosc. Radiat. Transfer 29, 259–266 (1983).
    [CrossRef]
  32. The authors, T. T. Charalampopoulos, G. Shu, are planning a paper on “Characterization of chain-like aggregates by dynamic light scattering.”
  33. G. Shu, “Theoretical and experimental studies of flame-generated agglomerates using light scattering,” Ph.D. dissertation (Louisiana State University, Baton Rouge Campus, Baton Rouge, La., 2000).

2002 (1)

2000 (2)

1995 (3)

G. M. Faeth, Ü. Ö. Köylü, “Soot morphology and optical properties in nonpremixed turbulent flame environments,” Combust. Sci. Technol. 108, 207–229 (1995).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1995).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

1992 (2)

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Progress Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

T. T. Charalampopoulos, D. W. Hahn, H. Chang, “Role of metal additives in light scattering from flame particulates,” Appl. Opt. 31, 6519–6528 (1992).
[CrossRef]

1991 (1)

1990 (1)

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

1989 (2)

P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
[CrossRef]

S. E. Pratsinis, S. V. R. Mastrangelo, “Material synthesis in aerosol reactors,” Chem. Eng. Prog. 85(5), 62–66 (1989).

1987 (1)

T. T. Charalampopoulos, “An automated light scattering system and a method for the measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

1985 (1)

H. Rohatschek, “Direction, magnitude, and causes of photophoretic forces,” J. Aerosol Sci. 16, 29–42 (1985).
[CrossRef]

1984 (1)

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News 62(32), 22–29 (1984).
[CrossRef]

1983 (1)

S. C. Lee, C. L. Tien, “Effects of soot shape on soot radiation,” J. Quant. Spectrosc. Radiat. Transfer 29, 259–266 (1983).
[CrossRef]

1980 (2)

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

1977 (1)

G. D. Ulrich, N. S. Subramanian, “Particle growth in flames III. Coalescence as a rate controlling process,” Combust. Sci. Technol. 17, 119–125 (1977).
[CrossRef]

1973 (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1969 (1)

I. A. Medalia, F. A. Heckman, “Morphology of aggregates II. Size and shape factors of carbon black aggregates from electron microscopy,” Carbon 7, 567–582 (1969).
[CrossRef]

1968 (1)

1967 (1)

O. Preining, “The Stokes diameter of ellipsoidal particles,” Atmos. Environ. 1, 271–285 (1967).
[CrossRef]

Allen, J.

J. Allen, R. B. Husar, E. S. Macias, “Aerosol size and shape distribution using a laser scattering spectrometer,” in Aerosol Measurements, F. S. Harris, W. H. Harlow, M. Lippman, W. E. Clark, M. D. Durham, eds., pp. 312–330.

Bach, D. R.

Bertram, D.

P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Hufman, Absorption and Scattering by Small Particles (Wiley, New York, 1983).

Chang, H.

T. T. Charalampopoulos, D. W. Hahn, H. Chang, “Role of metal additives in light scattering from flame particulates,” Appl. Opt. 31, 6519–6528 (1992).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Charalampopoulos, T. T.

T. T. Charalampopoulos, G. Shu, “Effects of polydispersity of chainlike aggregates on light-scattering properties and data inversion,” Appl. Opt. 41, 723–733 (2002).
[CrossRef] [PubMed]

G. Shu, T. T. Charalampopoulos, “Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols,” Appl. Opt. 39, 6713–6724 (2000).
[CrossRef]

G. Shu, T. T. Charalampopoulos, “Reciprocity theorem for the calculation of average properties of agglomerated particles,” Appl. Opt. 39, 5827–5833 (2000).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1995).
[CrossRef]

T. T. Charalampopoulos, D. W. Hahn, H. Chang, “Role of metal additives in light scattering from flame particulates,” Appl. Opt. 31, 6519–6528 (1992).
[CrossRef]

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Progress Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

T. T. Charalampopoulos, “An automated light scattering system and a method for the measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additive in sooting premixed flames,” in Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Sydney, Sydney, Australia, 1992), pp. 1007–1014.

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty Sixth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Naples, Naples, Italy, 1996), pp. 1851–1858.

The authors, T. T. Charalampopoulos, G. Shu, are planning a paper on “Characterization of chain-like aggregates by dynamic light scattering.”

Dobbins, R. A.

Faeth, G. M.

G. M. Faeth, Ü. Ö. Köylü, “Soot morphology and optical properties in nonpremixed turbulent flame environments,” Combust. Sci. Technol. 108, 207–229 (1995).
[CrossRef]

Hahn, D. W.

T. T. Charalampopoulos, D. W. Hahn, H. Chang, “Role of metal additives in light scattering from flame particulates,” Appl. Opt. 31, 6519–6528 (1992).
[CrossRef]

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additive in sooting premixed flames,” in Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Sydney, Sydney, Australia, 1992), pp. 1007–1014.

Heckman, F. A.

I. A. Medalia, F. A. Heckman, “Morphology of aggregates II. Size and shape factors of carbon black aggregates from electron microscopy,” Carbon 7, 567–582 (1969).
[CrossRef]

Hufman, D. R.

C. F. Bohren, D. R. Hufman, Absorption and Scattering by Small Particles (Wiley, New York, 1983).

Husar, R. B.

J. Allen, R. B. Husar, E. S. Macias, “Aerosol size and shape distribution using a laser scattering spectrometer,” in Aerosol Measurements, F. S. Harris, W. H. Harlow, M. Lippman, W. E. Clark, M. D. Durham, eds., pp. 312–330.

Kasper, G.

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983).

Köylü, Ü. Ö.

G. M. Faeth, Ü. Ö. Köylü, “Soot morphology and optical properties in nonpremixed turbulent flame environments,” Combust. Sci. Technol. 108, 207–229 (1995).
[CrossRef]

Lee, S. C.

S. C. Lee, C. L. Tien, “Effects of soot shape on soot radiation,” J. Quant. Spectrosc. Radiat. Transfer 29, 259–266 (1983).
[CrossRef]

Lou, W.

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1995).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

Macias, E. S.

J. Allen, R. B. Husar, E. S. Macias, “Aerosol size and shape distribution using a laser scattering spectrometer,” in Aerosol Measurements, F. S. Harris, W. H. Harlow, M. Lippman, W. E. Clark, M. D. Durham, eds., pp. 312–330.

Mastrangelo, S. V. R.

S. E. Pratsinis, S. V. R. Mastrangelo, “Material synthesis in aerosol reactors,” Chem. Eng. Prog. 85(5), 62–66 (1989).

Meakin, P.

P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
[CrossRef]

Medalia, I. A.

I. A. Medalia, F. A. Heckman, “Morphology of aggregates II. Size and shape factors of carbon black aggregates from electron microscopy,” Carbon 7, 567–582 (1969).
[CrossRef]

Megaridis, C. M.

Mulholland, G. W.

P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Pratsinis, S. E.

S. E. Pratsinis, S. V. R. Mastrangelo, “Material synthesis in aerosol reactors,” Chem. Eng. Prog. 85(5), 62–66 (1989).

Preining, O.

O. Preining, “The Stokes diameter of ellipsoidal particles,” Atmos. Environ. 1, 271–285 (1967).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Rohatschek, H.

H. Rohatschek, “Direction, magnitude, and causes of photophoretic forces,” J. Aerosol Sci. 16, 29–42 (1985).
[CrossRef]

Rudder, R. R.

Shaw, D. T.

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

Shon, S. N.

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

Shu, G.

Stagg, B. J.

B. J. Stagg, “Development of a technique to determine the temperature dependence of the refractive index of carbonaceous particulates,” Ph.D. dissertation (Louisiana State University, Baton Rouge Campus, Baton Rouge, La., 1992).

Subramanian, N. S.

G. D. Ulrich, N. S. Subramanian, “Particle growth in flames III. Coalescence as a rate controlling process,” Combust. Sci. Technol. 17, 119–125 (1977).
[CrossRef]

Tien, C. L.

S. C. Lee, C. L. Tien, “Effects of soot shape on soot radiation,” J. Quant. Spectrosc. Radiat. Transfer 29, 259–266 (1983).
[CrossRef]

Ulrich, G. D.

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News 62(32), 22–29 (1984).
[CrossRef]

G. D. Ulrich, N. S. Subramanian, “Particle growth in flames III. Coalescence as a rate controlling process,” Combust. Sci. Technol. 17, 119–125 (1977).
[CrossRef]

van Hulst, H. C.

H. C. van Hulst, Light Scattering by Small ParticlesDover, New York, 1981.

Zhang, Z.

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty Sixth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Naples, Naples, Italy, 1996), pp. 1851–1858.

Am. Ind. Hyg. Assoc. J. (2)

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

G. Kasper, S. N. Shon, D. T. Shaw, “Controlled formation of chain aggregates from very small metal oxide particles,” Am. Ind. Hyg. Assoc. J. 41, 288–296 (1980).
[CrossRef] [PubMed]

Appl. Opt. (5)

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Atmos. Environ. (1)

O. Preining, “The Stokes diameter of ellipsoidal particles,” Atmos. Environ. 1, 271–285 (1967).
[CrossRef]

Carbon (1)

I. A. Medalia, F. A. Heckman, “Morphology of aggregates II. Size and shape factors of carbon black aggregates from electron microscopy,” Carbon 7, 567–582 (1969).
[CrossRef]

Chem. Eng. News (1)

G. D. Ulrich, “Flame synthesis of fine particles,” Chem. Eng. News 62(32), 22–29 (1984).
[CrossRef]

Chem. Eng. Prog. (1)

S. E. Pratsinis, S. V. R. Mastrangelo, “Material synthesis in aerosol reactors,” Chem. Eng. Prog. 85(5), 62–66 (1989).

Combust. Sci. Technol. (2)

G. D. Ulrich, N. S. Subramanian, “Particle growth in flames III. Coalescence as a rate controlling process,” Combust. Sci. Technol. 17, 119–125 (1977).
[CrossRef]

G. M. Faeth, Ü. Ö. Köylü, “Soot morphology and optical properties in nonpremixed turbulent flame environments,” Combust. Sci. Technol. 108, 207–229 (1995).
[CrossRef]

J. Aerosol Sci. (1)

H. Rohatschek, “Direction, magnitude, and causes of photophoretic forces,” J. Aerosol Sci. 16, 29–42 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D (2)

W. Lou, T. T. Charalampopoulos, “On the electromagnetic scattering and absorption of agglomerated small spherical particles,” J. Phys. D 27, 2258–2270 (1995).
[CrossRef]

W. Lou, T. T. Charalampopoulos, “On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation,” J. Phys. D 28, 2585–2594 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

S. C. Lee, C. L. Tien, “Effects of soot shape on soot radiation,” J. Quant. Spectrosc. Radiat. Transfer 29, 259–266 (1983).
[CrossRef]

Langmuir (1)

P. Meakin, D. Bertram, G. W. Mulholland, “Collision between point masses and fractal aggregates,” Langmuir 5, 510–518 (1989).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

H. Chang, T. T. Charalampopoulos, “Determination of the wavelength dependence of the refractive indices of flame soot,” Proc. R. Soc. London Ser. A 430, 577–591 (1990).
[CrossRef]

Progress Energy Combust. Sci. (1)

T. T. Charalampopoulos, “Morphology and dynamics of agglomerated particulates in combustion systems using light scattering techniques,” Progress Energy Combust. Sci. 18, 13–45 (1992).
[CrossRef]

Rev. Sci. Instrum. (1)

T. T. Charalampopoulos, “An automated light scattering system and a method for the measurement of the index of refraction of soot particles,” Rev. Sci. Instrum. 58, 1638–1646 (1987).
[CrossRef]

Other (10)

http://www.lbl.gov/Publications/LDRD/1996/Charych.html

B. J. Stagg, “Development of a technique to determine the temperature dependence of the refractive index of carbonaceous particulates,” Ph.D. dissertation (Louisiana State University, Baton Rouge Campus, Baton Rouge, La., 1992).

The authors, T. T. Charalampopoulos, G. Shu, are planning a paper on “Characterization of chain-like aggregates by dynamic light scattering.”

G. Shu, “Theoretical and experimental studies of flame-generated agglomerates using light scattering,” Ph.D. dissertation (Louisiana State University, Baton Rouge Campus, Baton Rouge, La., 2000).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983).

H. C. van Hulst, Light Scattering by Small ParticlesDover, New York, 1981.

C. F. Bohren, D. R. Hufman, Absorption and Scattering by Small Particles (Wiley, New York, 1983).

D. W. Hahn, T. T. Charalampopoulos, “The role of iron additive in sooting premixed flames,” in Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Sydney, Sydney, Australia, 1992), pp. 1007–1014.

Z. Zhang, T. T. Charalampopoulos, “Controlled combustion synthesis of nanosized iron oxide aggregates,” in Twenty Sixth Symposium (International) on Combustion, The Combustion Institute, ed. (University of Naples, Naples, Italy, 1996), pp. 1851–1858.

J. Allen, R. B. Husar, E. S. Macias, “Aerosol size and shape distribution using a laser scattering spectrometer,” in Aerosol Measurements, F. S. Harris, W. H. Harlow, M. Lippman, W. E. Clark, M. D. Durham, eds., pp. 312–330.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the additive feeding system.

Fig. 2
Fig. 2

Concentric-tube burner.

Fig. 3
Fig. 3

Schematic diagram of the flame shroud.

Fig. 4
Fig. 4

Schematic diagram of the optical system.

Fig. 5
Fig. 5

Theoretical and experimental scattering cross sections versus scattering angle for nitrogen molecules normalized with respect to C vv(90°).

Fig. 6
Fig. 6

TEM of chainlike aggregates extracted from the central axis of the flame at 40 mm above the burner surface.

Fig. 7
Fig. 7

TEM of chainlike aggregates extracted from the central axis of the flame at 45 mm above the burner surface.

Fig. 8
Fig. 8

TEM of chainlike aggregates extracted from the central axis of the flame at 50 mm above the burner surface.

Fig. 9
Fig. 9

TEM of chainlike aggregates extracted from the central axis of the flame at 55 mm above the burner surface.

Tables (4)

Tables Icon

Table 1 Measurement Results of Light-Scattering Quantities and of Flame Temperature as a Function of Position in the Flame

Tables Icon

Table 2 Data-Inversion Results for Refractive Index, Size, and Number of Primary Particles per Agglomerate

Tables Icon

Table 3 Data-Inversion Results for Number Density and Volume Fraction of Agglomerates

Tables Icon

Table 4 Average Diameters of Primary Particles Determined from TEM Micrograph Analysis

Equations (53)

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1+ωC0Ei-ωC2j=1jiNpTijEj=Einc,i, i=1, 2, 3,, N,
ω=ε-1=n+ik2-1,
C0=13 |3-2ix2h11x|,
C2=i3 x2j1x,
Csca=4π3 R2x2j12x|ε-1|Rei=1Npj=1NpEi · TijEj*,
Cabs=4πR2j1xImε-1i=1Np |Ei|2,
Cext=4πR2j1xImε-1i=1NpEi · Einc,i.
Cvpθ=R2x2j12x|ε-1|2|V|2,
Chpθ=R2x2j12x|ε-1|2|H|2,
V=i=1Npexp-ikri cos βiEx,i,
H=i=1Npexp-ikri cos βicos θEy,i-sin θEz,i,
cos βi=cos θi cos θ+sin θi sin θ cosϕi-π2,
C¯extx=j1xxCextj1x+4πR2j1x×Imω i=1NpEinc,i* Eix-ikzixEi,
Cextk, Cextn=4πR2j1x×i=1NpEinc,i*ω Ein+ωnEi.
Cvpn=1|ω2|2|ω2|n Cvp+R2x2j12x|ω|2ReV* Vn,
Cvpx=1xj12xj12x Cvp+R2|ω|2xj12ReV* Vx.
C¯pp=18π202πdω 02πdψ 0π Cpp sin χdχ,
C¯pp=14π02πdψ 0π Cpp sin χdχ
Ippθ=I0ΔΩVnACpp¯θηoptτ,
τ=exp-nAC¯extL.
Kvv,eθ=C¯vvθC¯ext.
Rvvθ=C¯vvθC¯vv180-θ,
Rhh=C¯hhθC¯hh180-θ.
Rhv=C¯hvθC¯vvθ.
Kvv,eθx=1C¯extC¯vvθx-KvvθC¯extx.
Kvv,eθNp=12Kvv,eθ, Np+1-Kvv,eθ, Np-1.
Cvv=4π2m-12λ2N0233-4Rhv,
Chh=Cvv1-Rhvcos2θ+Rhv,
Chv=Cvh=CvvRhv,
Kvvθ=Ivvθlnτ L.
Rvvθ=IvvθIvv180°-θ,
Rhhθ=IhhθIhh180°-θ,
Rhvθ=IhvθIvvθ.
Cvv,flameθ=Cvv,methθIvv,flameθIvv,methθ
fv=nAπdp36.
Qiθ, n, k, x, Np=Miθ; i=1, 2, 3, 4,
S=i=14Qi0θ-MiθMiθ2,
Miθ=Qiθ, n0, k0, x0, Np0+Qin Δn+Qik Δk+Qix Δx+QiNp ΔNp; i=1, 2, 3, 4.
Qin Δn+Qik Δk+Qix Δx+QiNp ΔNp=Miθ-Qiθ, n0, k0, x0, Np0; i=1, 2, 3, 4.
Miθ=Qiθ, n, k, x, Np; i=1, 2, 3, 4.
Miθ+ΔMiθ=Qiθ, n+Δn, k+Δk, x+Δx, Np+ΔNp; i=1, 2, 3, 4
Qin Δn+Qik Δk+Qix Δx+QiNp ΔNp=ΔMi;i=1, 2, 3, 4.
nQiQinΔnn+kQiQikΔkk+xQiQixΔxx+NpQiQiNpΔNpNp=ΔMiMi; i=1, 2, 3, 4.
ΔM1M1, ΔM2M2, ΔM3M3, ΔM4M4T=AΔnn, Δkk, Δxx, ΔNpNpT,
A=nQ1Q1nkQ1Q1kxQ1Q1xNpQ1Q1NpnQ2Q2nkQ2Q2kxQ2Q2xNpQ2Q2NpnQ3Q3nkQ3Q3kxQ3Q3xNpQ3Q3NpnQ4Q4nkQ4Q4kxQ4Q4xNpQ4Q4Np.
Δnn=i=14 a1iΔMiMi,
Δkk=i=14 a2iΔMiMi,
Δxx=i=14 a3iΔMiMi,
ΔNpNp=i=14 a4iΔMiMi,
Δnn=i=14a1iΔMiMi21/2,
Δkk=i=14a2iΔMiMi21/2,
Δxx=i=14a3iΔMiMi21/2,
ΔNpNp=i=14a4iΔMiMi21/2.

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